Yeah, personally I would say that it's per kg bodyweight.
But I would also do my darndest to try write it, since "ng/kg" is kind of just nonsense. It makes it look like you could divide the grams out of that to get a fixed ratio, which is not correct at all.
But it is a fixed ratio.
If it was in pounds, metric tons, moles or atomic mass units... It doesn't change the ratio, the actual number.
Would it be acceptable to drop the unit all together?
"Lethal dose is 0.000000012 : 1 (substance : bodyweight)" (I made up the number).
I'm not sure if there is a better way of writing the ratio.
Could a fraction be more applicable?
"lethal dose is 1/600000 of bodyweight"
I'm sure it's written as ng/kg to show the base units are the same, and the rest is just "fiddling" scientific notation
would not work, as they are no mass unit. 1 mol of Botox does not have the same weight as 1 mol of human (If that is defined at all, as organisms are no pure substances).
Yeah - the dose is the poison (if you drink enough water it becomes toxic), so if you are talking precisely you need to describe the concentration of a substance in which it is likely lethal to a person, and that's typically expressed as mass of a substance per mass of bodyweight. A lot of the time you will also see this expressed as an "LD50" value; the dose at which you'd expect 50% of people to die. This accounts for the fact that people's metabolisms vary quite widely.
~1ng/kg ~= 0.08ug for a typical (~80kg) person, which is a very tiny amount - whatever you are talking about is incredibly toxic.